# Nonexponential tunneling decay of a single ultracold atom

## TL;DR

This paper analytically investigates the nonexponential tunneling decay of ultracold single atoms, revealing conditions under which deviations from exponential decay occur, with potential for experimental observation.

## Contribution

It introduces an exact analytical approach to study decay dynamics and identifies the key ratio R that determines decay behavior deviations.

## Key findings

- Decay approximates exponential for R<0.3 in initial lifetimes
- Nonexponential decay occurs around R~1 after multiple lifetimes
- Conditions for experimental verification depend on potential parameters

## Abstract

By using an exact analytical approach to the time evolution of decay we investigate the tunneling decay of ultracold single atoms, to discuss the conditions for deviations of the exponential decay law. We find that $R$, given by the ratio of the energy of the decaying fragment $\mathcal{E}_r$ to its corresponding width $\Gamma_r$, is the relevant quantity in this study. When $R$ is less than $0.3$ the decay of the atom goes to a good approximation for the first few lifetimes as $\exp(-\Gamma_rt/2\hbar)t^{-3/2}$. We also find that for values of $R \sim 1$, the nonexponential behavior occurs in a post-exponential regime that goes as $t^{-3}$ after around a dozen of lifetimes. The above conditions depend on suitable designed potential parameters and suggest that for values $R \lesssim 1$, the experimental verification of nonexponential decay might be possible.